Cellular lipid droplets are the least studied and least understood cellular organelles in eukaryotic and prokaryotic cells. Despite a significant body of research studying the physiology of lipid droplets it has not yet been possible to fully determine the composition of individual cellular lipid droplets. In this paper we use Raman spectroscopy on single cellular lipid droplets and least-squares fitting of pure fatty acid spectra to determine the composition of individual lipid droplets in cells after treatment with different ratios of oleic and palmitic acid. We validate the results of the Raman spectroscopy-based single lipid droplet analysis with results obtained by gas chromatography analysis of millions of cells, and find that our approach can accurately predict the relative amount of a specific fatty acid in the lipid droplet. Based on these results we show that the fatty acid composition in individual lipid droplets is on average similar to that of all lipid droplets found in the sample. Furthermore, we expand this approach to the investigation of the lipid composition in single cellular peroxisomes. We determine the location of cellular peroxisomes based on two-photon excitation fluorescence (TPEF) imaging of peroxisomes labeled with the green fluorescent protein, and successive Raman spectroscopy of peroxisomes. We find that in some cases peroxisomes can produce a detectable CARS signal, and that the peroxisomal Raman spectra exhibit an oleic acid-like signature.